I know about the problems on installing and upgrading DNN on Plesk.  But the issue is mostly on the special Plesk settings.  So after a Plesk Upgrade often the Permissions are changed, and this runs into issues on upgrading DNN.  Plesk created Databases are not on dbo Schema and uses often the username as the schema.  This needed a special setup of the web.config file and the databaseOwner on the web.config file has set to the used Schema.

SqlDataProviders of 3rd partity modules often have not well formes functions, procedures and views, this makes issues on upgrades too if the SQL Schema is not dbo.

So I could not say the issues are related to DNN, all those issues are related to Parallels or to the admin who setting up the hosting or Plesk infrastructure.  The good new are that on Parallels Plesk on Version 10.4.x you could create a normal folder as your DNN root folder and inherit the domain to this folder, and you could change all permissions over the Plesk panel.